{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7XN3ZM5DY33EVFZET7ZDNAOWKH","short_pith_number":"pith:7XN3ZM5D","schema_version":"1.0","canonical_sha256":"fddbbcb3a3c6f64a97249ff23681d651efdbb1b7084fdffe17c40ede5d031b86","source":{"kind":"arxiv","id":"2411.10850","version":4},"attestation_state":"computed","paper":{"title":"Asymptotic evaluations of generalized Bessel function of order zero related to the p-circle lattice point problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Masaya Kitajima","submitted_at":"2024-11-16T17:59:14Z","abstract_excerpt":"Let $p$ and $r$ be positive real numbers. Then, we consider the lattice point problem of the closed curve $p$-circle $\\{x\\in\\mathbb{R}^{2}|\\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\\}$ which is a generalization of the circle ($p=2$). Following the harmonic analytic approach of S. Kuratsubo and E. Nakai for the case of a circle, we need to investigate properties of appropriately generalized Bessel functions for $p$ in order to tackle the problem. Thus, in this paper, we derive asymptotic evaluations of the generalized Bessel function of order zero, such as uniformly asymptotic estimates on compact sets on"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2411.10850","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-16T17:59:14Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"e300c2fac958fa059e20b3e34fe5d4900485b509d5c9ac232a73e2a171b55609","abstract_canon_sha256":"21c1c7d65819c0062c9a20af5f34df957b9f33c663c00b6bec0f314a4c7392f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:03:02.198833Z","signature_b64":"EsRpnOpr/SrD7ul9EldcJPcQujpskR1HxrIsp2SVTP7IhNAuWjgjCHPN2EUVlpbpBe7/jX8jWRAsdzsLJwIUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fddbbcb3a3c6f64a97249ff23681d651efdbb1b7084fdffe17c40ede5d031b86","last_reissued_at":"2026-07-05T11:03:02.198360Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:03:02.198360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic evaluations of generalized Bessel function of order zero related to the p-circle lattice point problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Masaya Kitajima","submitted_at":"2024-11-16T17:59:14Z","abstract_excerpt":"Let $p$ and $r$ be positive real numbers. Then, we consider the lattice point problem of the closed curve $p$-circle $\\{x\\in\\mathbb{R}^{2}|\\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\\}$ which is a generalization of the circle ($p=2$). Following the harmonic analytic approach of S. Kuratsubo and E. Nakai for the case of a circle, we need to investigate properties of appropriately generalized Bessel functions for $p$ in order to tackle the problem. Thus, in this paper, we derive asymptotic evaluations of the generalized Bessel function of order zero, such as uniformly asymptotic estimates on compact sets on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10850","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.10850/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2411.10850","created_at":"2026-07-05T11:03:02.198418+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.10850v4","created_at":"2026-07-05T11:03:02.198418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.10850","created_at":"2026-07-05T11:03:02.198418+00:00"},{"alias_kind":"pith_short_12","alias_value":"7XN3ZM5DY33E","created_at":"2026-07-05T11:03:02.198418+00:00"},{"alias_kind":"pith_short_16","alias_value":"7XN3ZM5DY33EVFZE","created_at":"2026-07-05T11:03:02.198418+00:00"},{"alias_kind":"pith_short_8","alias_value":"7XN3ZM5D","created_at":"2026-07-05T11:03:02.198418+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.03331","citing_title":"Generalized Hardy's identity for the astroid-type p-circle lattice point problem","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH","json":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH.json","graph_json":"https://pith.science/api/pith-number/7XN3ZM5DY33EVFZET7ZDNAOWKH/graph.json","events_json":"https://pith.science/api/pith-number/7XN3ZM5DY33EVFZET7ZDNAOWKH/events.json","paper":"https://pith.science/paper/7XN3ZM5D"},"agent_actions":{"view_html":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH","download_json":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH.json","view_paper":"https://pith.science/paper/7XN3ZM5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.10850&json=true","fetch_graph":"https://pith.science/api/pith-number/7XN3ZM5DY33EVFZET7ZDNAOWKH/graph.json","fetch_events":"https://pith.science/api/pith-number/7XN3ZM5DY33EVFZET7ZDNAOWKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH/action/storage_attestation","attest_author":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH/action/author_attestation","sign_citation":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH/action/citation_signature","submit_replication":"https://pith.science/pith/7XN3ZM5DY33EVFZET7ZDNAOWKH/action/replication_record"}},"created_at":"2026-07-05T11:03:02.198418+00:00","updated_at":"2026-07-05T11:03:02.198418+00:00"}